The generator matrix

 1  0  1  1  1 X^2+X  1  1
 0  1 X+1 X^2+X X^2+1  1  0 X^2+X
 0  0 X^2  0 X^2  0  0 X^2
 0  0  0 X^2 X^2 X^2 X^2 X^2

generates a code of length 8 over Z2[X]/(X^3) who´s minimum homogenous weight is 6.

Homogenous weight enumerator: w(x)=1x^0+33x^6+64x^7+61x^8+64x^9+30x^10+2x^12+1x^14

The gray image is a linear code over GF(2) with n=32, k=8 and d=12.
As d=13 is an upper bound for linear (32,8,2)-codes, this code is optimal over Z2[X]/(X^3) for dimension 8.
This code was found by Heurico 1.16 in 0.000393 seconds.